Context. New spectroscopic observations in the far-infrared (IR) range are expected from future planned missions. Although water ice is the only species detected so far in interstellar ices in this range, the presence of ice mixtures requires laboratory characterization of the corresponding spectra. Aims. We present an investigation on far-IR spectra of binary ice mixtures relevant in various astrophysical environments. The foremost goal is to compare the spectroscopic features of the ice mixtures to those of pure ices, and to search for changes in peak frequencies, intensities, and band strengths of the main bands. Methods. Mixtures H 2 O:CH 3 OH and H 2 O:NH 3 of different ratios have been deposited on a diamond substrate at astrophysically relevant conditions. We measured the spectra in the near-and mid-IR regions to derive ice column densities that were subsequently used to calculate the apparent band strengths in the far-IR region. We also designed theoretical models to study these mixtures and to predict their spectra. Results. We recorded spectra of amorphous phases for H 2 O:CH 3 OH mixtures of different compositions, that is 1:1, 3:1, and 10:1 at 8 K, and compared these mixtures to those obtained after warming. This process involves the appearance of new spectral features and changes in band shapes and band strengths. We also compared the spectra to those of the pure species and to theoretical predictions. We measured apparent band strengths for all the observed features. For H 2 O:NH 3 mixtures, the ratios selected were 3:1, 1:1, and 1:3. In this case the spectral variations are even more marked than for the water:methanol samples. Conclusions. Band strengths in the far-IR are missing in astrophysics literature for ice mixtures. The results presented here are valuable for detecting the presence and composition of such mixtures from future space observations in this spectral region.